Method and device for determining the charge that can be drawn from an energy accumulator

ABSTRACT

A device for ascertaining the charge able to be drawn from an energy store, in particular a battery, up to a specified cutoff, is provided. A particularly precise charge prediction may be achieved if a mathematical energy store model is used, which mathematically represents the electrical properties of the energy store and with the aid of which a charge predictor calculates the charge able to be drawn in the case of a specified discharge current. The charge predictor is connected with an estimator for a state variable and parameter, which estimator ascertains state variables and/or parameters for the mathematical energy store model from current operating performance quantities of the energy store.

FIELD OF THE INVENTION

The present invention relates to a device for ascertaining the charge able to be drawn from an energy store, in particular a battery, up to a specified cutoff, as well as a corresponding method.

BACKGROUND INFORMATION

In the case of electrical energy stores such as batteries, for example, the current charge able to be drawn is an important variable, since it expresses the energy reserve still available before a minimum capacity required of the energy store is undershot. Especially in the field of automotive technology, a precise prediction of the charge able to be drawn is more decisive than the knowledge of the current charge state of the battery defined via the average acid concentration in the lead accumulator, since the latter only provides information about the charge already drawn in relation to the full charge, but not, however, about the amount of charge that is still able to be drawn.

The entire charge still able to be drawn immediately determines the availability of the electrical loads connected to the energy store. The knowledge of the charge able to be drawn may additionally be used for measures of open-loop or closed-loop control technology such as are used, for example, for an energy management system in a vehicle. This makes it possible, for example, to initiate, in time before reaching a minimum charge reserve, consumption-reducing measures such as switching off or dimming less important loads.

A method is described in published European patent document EP-0376967 to determine the charge able to be drawn from an energy store. In this instance, the charge able to be drawn is estimated via empirically ascertained characteristics maps, which are stored in a processing unit, as a function of a constant discharging current, of the battery temperature and of aging effects on the basis of the Peukert formula. To be sure, this makes it possible to ascertain the charge able to be drawn up to a cutoff, which is characterized by the complete discharge of the energy store; however, it is not possible to determine the charge able to be drawn before undershooting a specified minimum terminal voltage or before undershooting a minimum capacity of the energy store. Moreover, determining the charge able to be drawn on the basis of the Peukert formula is relatively imprecise, since different effects influencing the state of the cutoff such as, e.g., an active mass loss at the electrodes due to the ageing of the battery or the formation of ice at the electrodes at low temperatures are not taken into account.

It is therefore an objective of the present invention to provide a device and a method for ascertaining the charge able to be drawn from an energy store, which allow for a very precise determination of the charge able to be drawn before meeting a specified cutoff criterion.

SUMMARY

The present invention provides a charge predictor, i.e., a device for calculating the charge able to be drawn, which calculates the charge able to be drawn from the energy store with the help of a mathematical energy store model by taking a specified discharge current characteristic and temperature characteristic into account. The energy store model in this instance is a mathematical model, which uses different mathematical models to represent the electrical properties of the energy store that are based on different physical effects. The mathematical models describe functional relationships between variables of state such as, for example, voltages, currents, temperature, etc., and include different parameters.

The charge computation carried out by the charge predictor takes place starting from the current state of the energy store. Therefore, the mathematical models stored in the charge predictor are first initialized to the current operating state of the energy store. For this purpose, a state variable and parameter estimator is provided, which ascertains the state variables and if applicable also parameters of the energy store model from the current performance quantities such as, for example, the voltage, the current and the temperature of the energy store. For those state variables of the energy store that cannot be measured directly during operation, it is possible to use, for example, a known Kalman filter as a state variable and parameter estimator. Starting from this initialization state, the charge predictor then calculates the charge able to be drawn up to a specified cutoff, i.e. before meeting one or several specified cutoff criteria, which will be explained in detail below.

The energy store model includes in the case of a battery at least one model for the internal resistance R_(i) of the battery, an acid diffusion resistance R_(k) and a charge transfer polarization U_(D).

The state and parameter estimator ascertains as state variables Z at least an open-circuit voltage U_(C0) of the battery and a concentration polarization U_(k). To the extent that the battery capacity and thus also the acid capacity C₀ of the battery used is unknown, this is to be calculated as well. For this purpose, the state variable and parameter estimator ascertains at least the parameters R_(i025), U_(e,grenz), R_(k025), U_(DO25) and C₀. These parameters will be explained in detail below.

The cutoff criterion, up to which the charge able to be drawn is calculated, may be, for example, the reaching or undershooting of a specified minimum electrolyte voltage U_(ekrit), a minimum terminal voltage U_(Battmin) or the reaching of a specified minimum capacity U_(Lastmin). According to an example embodiment of the present invention, the charge able to be drawn is calculated until at least two, or all three, of the mentioned cutoff criteria are reached or undershot.

The cutoff criterion of the minimum electrolyte voltage U_(ekrit) is fulfilled if the electrolyte voltage U_(e) falls below the specified minimum electrolyte voltage U_(ekrit). For this purpose, the specified electrolyte voltage U_(ekrit) preferably takes into account the active mass loss due to battery ageing and/or the formation of ice at the electrodes at low temperatures.

The cutoff criterion of the minimum terminal voltage U_(Battmin) is fulfilled if the terminal voltage U_(Batt) falls below the specified minimum terminal voltage U_(Battmin).

The criterion of the minimum capacity is met if a line voltage such as, for example, the voltage at a load powered by the energy store would sink below a specified threshold value if the energy store would have the load placed on it over a specified time period. To establish whether the load voltage in a specified load current characteristic would sink below a specified threshold value, a voltage predictor is provided, which ascertains the associated load voltage as a function of the load current characteristic. In a motor vehicle it is thus possible to ascertain how much charge is still able to be drawn from the motor vehicle battery given a specified discharge current and battery temperature characteristic before there is only an amount of charge remaining that is sufficient for the line voltage at an electrical load to be connected at a specified load current characteristic not to fall below a specified threshold value. In the case of a motor vehicle electrical system, this is especially necessary so as to prevent more charge from being taken from the battery than is required, for example, for a new starting procedure.

Alternatively, other cutoff criteria may be defined as well.

At specified temporal intervals, the charge predictor repeats the ascertainment of the charge able to be drawn from the energy store, in each case taking current values for the discharge current I_(Batt,entl) and the energy store temperature T_(Batt,entl) into account. The charge predictor may also be capable of determining the time until the specified cutoff criterion is met.

The state and parameter estimator works on the basis of the same energy store model as the charge predictor.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic representation of a device according to the present invention for ascertaining the charge able to be drawn from a battery, the device having a charge predictor and a voltage predictor.

FIG. 2 is an equivalent circuit diagram for a lead accumulator.

FIG. 3 a is a flow chart illustrating the method steps in calculating the charge able to be drawn using a charge predictor.

FIGS. 3 b and 3 c show a flow chart illustrating the checking of different cutoff criteria.

FIG. 3 d is a flow chart illustrating the method steps in calculating a minimum battery voltage using a charge predictor.

FIG. 4 is a graph illustrating the dependence of the electrolyte voltage on different physical effects.

DETAILED DESCRIPTION

1. Device for Ascertaining the Charge Able to be Drawn

FIG. 1 shows a block diagram of a device for calculating the charge able to be drawn from a battery, e.g., a vehicle battery. This includes a state variable and parameter estimator 1, a charge predictor 2 and a voltage predictor 3. The device is capable of calculating the charge able to be drawn from the battery (not shown) starting from a current battery state U_(Batt), I_(Batt), T_(Batt) and a specified discharge current characteristic I_(Batt,entl) until a specified cutoff is reached. The discharge current characteristic I_(Batt,entl) in this case may be an arbitrarily specified current characteristic or a constant current (I_(Batt)).

Charge predictor 2 and voltage predictor 3 include a mathematical battery model, which describes the electrical properties of the vehicle battery. Knowing the current performance quantities of the battery, that is, current battery voltage U_(Batt), current battery current I_(Batt) and current battery temperature T_(Batt), as well as taking into account a specified discharge current characteristic I_(Batt,entl) and a specified temperature characteristic T_(Batt,entl), it is thus possible to calculate the charge able to be drawn from the battery Q_(e,Ukrit), Q_(e,UBattmin), Q_(e,ULastmin) until three different cutoff criteria (which are conjunctively combined in the present example) are met. Discharge current characteristic I_(Batt,entl) and temperature characteristic T_(Batt,entl) during discharge may either be specified by a control unit (not shown) or may be ascertained from the current performance quantities of the battery U_(Batt), I_(Batt), T_(Batt).

Charge predictor 2 and voltage predictor 3 include a mathematical battery model, which mathematically describes the electrical properties of the vehicle battery and is based on the equivalent circuit diagram for a lead accumulator shown in FIG. 2.

2. Equivalent Circuit Diagram of a Lead Accumulator

FIG. 2 shows the equivalent circuit diagram of a lead accumulator. As is customary, the counting direction of battery current I_(Batt) was chosen to be positive for charging and negative for discharging. The individual state variables and components are as follows, from left to right:

-   R_(i)(U_(C0),U_(e),T_(Batt)) Ohmic internal resistance, dependent on     open-circuit voltage U_(C0), electrolyte voltage U_(e) and acid     temperature T_(Batt) -   U_(Ri) Ohmic voltage drop -   C₀ Acid capacity -   U_(C0) Open-circuit voltage -   R_(F) (U_(C0), T_(Batt)) Acid diffusion resistance, dependent on     open-circuit voltage U_(CO) (degree of discharge) and acid     temperature T_(Batt) -   τ_(k)=R_(k)*C_(k) Time constant of acid diffusion (is assumed to be     constant in the order of magnitude of 10 min) -   U_(k) Concentration polarization -   U_(e)=U_(C0)+U_(k) Electrolyte voltage -   ΔU_(Nernst)(U_(e),T_(Batt)) Voltage difference between the terminal     voltage and electrolyte voltage U_(e), dependent on electrolyte     voltage U_(e) and acid temperature T_(Batt) -   U_(D) (I_(Batt), T_(Batt)) Stationary charge transfer polarization,     dependent on battery current I_(Batt) and acid temperature T_(Batt) -   U_(Batt) Terminal voltage of the battery

The individual variables are attributable to different physical effects of the battery, which are briefly explained in the following:

Voltage U_(Ri) is the ohmic voltage drop at internal resistance R_(i) of the battery, which in turn depends on open-circuit voltage U_(C0), electrolyte voltage U_(e) and acid temperature T_(Batt).

Open-circuit voltage U_(C0) is proportional to the average acid concentration in the battery and is equal to the terminal voltage of the battery if the acid concentration following a rest phase of the battery is of the same magnitude everywhere.

Concentration polarization U_(k) takes into account the deviation of the acid concentration at the location of the reaction, i.e. at the electrodes, from the average value in the battery. As the battery discharges, the lowest acid concentration exist in the pores of the electrodes, since the acid is consumed there and new acid must first continue to flow in from the electrolyte.

Electrolyte voltage U_(e) takes into account the deviation of open-circuit voltage U_(C0) by the concentration polarization as a function of the acid concentration at the location of the reaction. The equation U_(e)=U_(C0)+U_(k) applies in this connection.

The term ΔU_(Nernst)(U_(e),T_(Batt)) describes the voltage difference between the electrode potential and the electrolyte voltage, which in turn depends on the local acid concentration at the location of the reaction and on acid temperature T_(Batt).

Stationary charge transfer polarization U_(D)(I_(Batt),T_(Batt)) takes into account an electrical transfer resistance between a first electrode of the battery and the electrolyte and between the electrolyte and the second electrode of the battery, and is in turn dependent on battery current I_(Batt) and acid temperature T_(Batt).

The diffusion of the acid from the electrolyte to the location of the reaction, i.e. to the electrodes, during discharge is described by acid diffusion resistance R_(k)(U_(C0), T_(Batt)), which in turn is dependent on open-circuit voltage U_(C0) and acid temperature T_(Batt).

3. The Mathematical Energy Store Model

The mathematical energy store model includes several models, which describe the ohmic internal resistance of the battery R_(i)(U_(C0),U_(e),T_(Batt)), acid diffusion resistance R_(k)(U_(C0),T_(Batt)), voltage difference ΔU_(Nernst)(U_(e),T_(Batt)) between the electrode potential and the electrolyte voltage, and stationary charge transfer polarization U_(D) (I_(Batt),T_(Batt)). Alternatively, more or fewer mathematical models may be taken into account as well. For the individual variables listed below, other mathematical models may be applied as well.

3.1. Ohmic Internal Resistance: R _(i)(U _(CO),U_(e),T_(Batt))⁼ R _(i0)(T _(Batt))*(1+R _(i, fakt)(U _(c0max) −U _(C0))/(U _(e) −U _(e,grenz))) where R _(i0)(T _(Batt))=R _(i025)/(l+TK _(Lfakt)*(T _(Batt)−25° C.)) Where

-   R_(i025) Ohmic internal resistance at full charge and T_(Batt)=25°     C. -   TK_(Lfakt) Temperature coefficient of the battery conductivity -   R_(i, fakt) Characteristics map parameter -   U_(COmax) Maximum open-circuit voltage of the completely charged     battery -   U_(e,grenz) Electrolyte voltage at cutoff (dependent on ageing)     3.2. Acid Diffusion Resistance

To approximate acid diffusion resistance R_(k), for example, the following model may be used: R _(k)(U _(CO) ,T _(Batt))=R _(k0)(T _(Batt))*(1+R _(k,fakt1)*(U _(C0max) −U _(C0))+R _(k, fakt2)*(U _(C0max) −U _(C0))² +R _(k,fakt3)*(U _(C0max) −U _(C0))³) where R _(k0)(T _(Batt))=R _(k025)*exp(−(E _(Rk0) /J)/8.314*(1/(273.15+T _(Batt)/° C.)−1/298.15))(Arrhenius approach) and

-   R_(k025) Acid diffusion resistance at full charge and T_(Batt)=25°     C. -   E_(rk0) Activation energy -   R_(k,fakt1), R_(k,fakt2), -   R_(k,fakt3) Polynomial coefficients     3.3 Voltage Difference ΔU_(Nernst) between the Electrode Potential     and Electrolyte Voltage U_(e)

For the voltage difference between the electrode potential and the electrolyte voltage, the following model may be used, for example: ΔU _(Nernst)(U _(e) ,T _(Batt))=alpha*exp(−(U _(e) −U _(ekn))/beta)+TK _(U00)*(T _(Batt)−25° C.) where

-   alpha, beta, -   U_(ekn) Characteristics parameter -   TK_(U00) Temperature coefficient of the electrode potential     3.4. Stationary Charge Transfer Polarization

For stationary charge transfer polarization UD, the following model may be used: U _(D)(I _(Batt) ,T _(Batt))=U _(DO)(T _(Batt))*ln(I _(Batt) /I _(DO)) where U _(DO)(T _(Batt))=U_(D025)*(1+TK _(UDO1)*(T _(Batt)−25° C.)+TK _(UD02)*(T _(Batt)−25° C.)² +TK _(UDO3)*(T _(Batt)−25° C.)³)

-   U_(D025) Stationary charge transfer voltage at I_(Batt)=e*I_(D0) and     T_(Batt)=25° C. -   I_(DO) Charge transfer current for U_(D)=OV -   TK_(UD01), TK_(UD02), -   TK_(UDO2) Temperature coefficients of the first, second and third     order of the charge transfer polarization     3.5. Influence of the Acid Stratification in the Battery

An acid stratification is built up in the case of lead batteries having a liquid electrolyte if the battery, starting from a low charge state, i.e., a low average acid concentration, is charged using high current. Due to the high charging current, acid of high concentration forms in the region of the electrodes (location of reaction), which due to its higher specific gravity sinks downward such that the acid of low concentration remains in the upper region. Because of this, in the event of acid stratification, the battery behaves like a battery of reduced capacity (and thus resulting in reduced charge able to be drawn), since only the lower battery region having the high acid concentration still participates in the reaction. In addition, due to the increased acid concentration in the lower region, the electrode potential is raised above the value of an unstratified battery. Since open-circuit voltage U_(C0) and acid capacity C₀ are ascertained and adapted by state variable and parameter estimator 1, the effect of the acid stratification on the charge able to be drawn is already implicitly taken into account in the charge prediction by charge predictor 2. The method thus also takes into account the reduction of the charge able to be drawn in the case of batteries having acid stratification.

4. Calculation of the Charge Able to be Drawn From the Energy Store

FIG. 3 a shows the calculation of charge Q_(e) able to be drawn from a vehicle battery. To this end, charge predictor 2 performs a numeric calculation and ascertains state variables U_(C0), U_(k), U_(e), ΔU_(Nernst), U_(Ri) and U_(Batt) of the battery model from FIG. 2. In detail, the calculation is performed as follows:

In block 10, charge q_(k) drawn from the battery in a time step t_(sample) is calculated for an assumed discharge current characteristic I_(Batt,entl) and iteratively added. Discharge current characteristic I_(Batt,entl), for example, may be constant and correspond to battery current I_(Batt) or may be an arbitrarily specified current characteristic. The following equations apply: q _(k+1) ′=q _(k′) +I _(Batt,entl) *t _(sample) t _(k+1) ′=t _(k) ′+t _(sample)

The starting values q₀′ and t₀′ for this calculation are: q ₀=0,t ₀′=0

This iterative calculation is continued until a specified cutoff criterion is fulfilled. The charge able to be drawn from the battery is then Q_(e)=q_(k+1)′, and the time still remaining before meeting the cutoff criterion at the specified discharge current I_(Batt,entl) is t_(e)=t_(k+1)′.

In blocks 11 through 15, stationary charge transfer polarization U_(D)(I_(Batt,entl),T_(Batt,entl)), open-circuit voltage U_(C0,k+1)′, concentration polarization U_(k,k+1)′, electrolyte voltage U_(e,k+1)′, the value ΔU_(Nernst,k+1)′, ohmic voltage drop U_(Ri,k+1)′ and battery voltage U_(Batt,k+1)′ are calculated. The equations in detail are: U _(C0,k+1′) =U _(C0,0′) +q _(k+1′) /C ₀′ Starting values: U_(C0,0)′=U_(C0), C₀′=C₀ U _(k,k+1) ′=U _(k,k)′+(I _(Batt, entl) *R _(k)(U _(C0,k+1) ′,T _(Batt,entl))−U _(k,k)′)*t _(sample) /tau _(k) U _(e,k+1) ′=U _(C0,k+1) ′+U _(k,k+1)′ ΔU_(Nernst,k+1′)=alpha*exp(−(U _(e,k+1) ′U _(ekn))/epsilon)+TK_(U00)*(T _(Batt,entl)−25° C.) Starting values: U_(k0)′=U_(k), R_(k025)′=R_(k025) U _(Ri,k+1) ′=R _(i)(U _(C0,k+1) ′,U _(C0,k+1) ′,T _(Batt, entl))*I _(Batt,entl) Starting values: R_(i025)′=R_(i025),U_(e,grenz)′=U_(e,grenz) U _(Batt,k+1) ′=U _(Ri,k+1) ′+U _(e,k+1) ′+°U _(Nernst,k+1) ′+U _(D)′

Here, U_(Batt,k+1)′ having index k+1 is a new value following an iteration. The iteration is performed until a specified cutoff criterion, in the present example simultaneously three different cutoff criteria, is fulfilled.

The comparison of the state variables with the different cutoff criteria is represented in FIGS. 3 b and 3 c. The first cutoff criterion is the reaching of a critical electrolyte voltage U_(e,krit), which is determined by the acid concentration in the electrolyte, the battery temperature T_(Batt,entl) and a voltage limitation by active mass loss of the battery electrodes ΔU_(e,grenz). In step 21 of FIG. 3 b, a check is performed for each iteration step k as to whether the electrolyte voltage U_(e,k+1)′ is smaller than or equal to the critical electrolyte voltage. If this is the case, then in step 22 a corresponding flag flag_(Ue,krit) is set to logical “1” (TRUE). The charge able to be drawn Q_(e) in the case of this cutoff criterion is therefore Q_(e,Uekrit)=q_(k+1)′, and the period of time before the cutoff criterion is met is t_(e,Uekrit)−t_(k+1)′.

In parallel to step 21, a check is performed in step 24 as to whether a second cutoff criterion has been met. To this end, a check is performed to determine whether battery voltage U_(Batt,k+1′) is smaller than or equal to a specified minimum battery voltage U_(Batt,min). If this is the case, then again a specific flag identified as flag_(UBattmin) is set to TRUE. The charge able to be drawn Q_(e,Ubattmin)=q_(k+1)′ and the time t_(e,UBattmin) required to reach this cutoff criterion is t_(e,Ubattmin)=t_(k+1).

Finally, in step 26 (see FIG. 3 c), a check is performed as to whether the third cutoff criterion, that is, a required minimum capacity of the battery, has been reached. To this end, a check is performed to determine whether a load voltage U_(Last) dropping at a specifiable load would during a specified load current characteristic I_(Last) become smaller than or equal to a minimum load voltage U_(Last,min) if the load were switched on at a specifiable time. Load voltage U_(Last) is thus the voltage that ensues at the load or e.g. at the battery if the load having a specified load current characteristic I_(Last) were switched on for a specified period of time t_(Last). The background for this calculation is that for the time period t_(Last) it is to be ensured that the line voltage (or load voltage) does not fall below a specified minimum value and that the load during its operating time t_(Last) is sufficiently supplied. For calculating load voltage U_(Last), which sets in after a specified on-time t_(Last), voltage predictor 3 is provided. Using the known models for state variables U_(C0),U_(k),U_(e), ΔU_(Nernst), U_(Ri) and U_(D), the latter calculates battery voltage U_(Batt) (step 36) at a specified load current characteristic I_(Last) and via a specified load on-time t_(Last). The minimum value of battery voltage U_(Batt) from all iteration steps (step 37) following the expiration of load on-time t_(Last) (step 38) is equal to the load voltage U_(Last) (step 39).

In blocks 30 through 36 (see FIG. 3 d), voltage predictor 3 uses the same calculation models as the charge predictor for calculating the battery state variables with the difference that the calculation is based on a load current characteristic I_(Last). Load current characteristic I_(Last) for example is the current which a load such as for example the starter motor in a motor vehicle requires for operation. Load current characteristic I_(Last) and on-time t_(Last) may, for example, be specified by a control unit. The following equation applies: q _(k+1) ″=q _(k) ″+I _(Last) *t _(sample) t _(k+1) ″=t _(k) ″+t _(sample)

In block 26, minimum battery voltage U_(Last) occurring in the load simulation is compared to a threshold value U_(Last,min) and it is established whether minimum load voltage U_(Last) is smaller than or equal to voltage U_(Last,min).

Voltage predictor 3 calculates minimum voltage U_(min) at a specified load current I_(Last) in every iteration step of charge predictor 2. If the simulation yields the result that the minimum capacity has been reached (U_(Last)<=U_(Last,min)), then a specific flag identified as flag_(ULastmin) is set to TRUE. The charge Q_(e) able to be drawn up to this third cutoff criterion is: Q _(e,ULastmin) =q _(k+1)′.

In the case of specified discharge current I_(Batt,entl), the minimum capacity of the battery is reached within a time t _(e,ULastmin) =t _(k+1)′(block 27).

If the cutoff criteria have not been met in steps 21, 24 and 26, then, just as after blocks 22, 25 and 27, a check is performed in step 28 as to whether all three cutoff criteria are fulfilled simultaneously. If this is the case, then the minimum value of the charges able to be drawn Q_(e,Uekrit), Q_(e,UBattmin), Q_(e,ULastmin) are output as the maximum charge able to be drawn. At the same time, the associated duration t_(e) may also be output. If it is not the case, the calculation is continued.

In the case of a constant discharge current I_(Batt,entl)=constant and a constant temperature T_(Batt,entl)=constant, state variables U_(C0)′ and U_(k)′ as well as battery voltage U_(Batt)′ may also be calculated analytically such that the computing-time-intensive iterative calculation according to FIG. 3 a on the part of charge predictor 2 may be eliminated.

5. Definition of the First Cutoff Criterion

The charge able to be drawn from a battery depends essentially on the acid contained in the electrolyte. In addition, the discharge termination secondly also depends on the active mass (Pb, PbO₂ in the case of lead accumulators) in the electrodes of the battery accessible during the discharge process and thirdly on the electrolyte icing at low temperatures. The precision of the charge able to be drawn may be substantially improved by taking into account at least one of the above-mentioned effects.

5.1. Acid Limitation

In the case of new batteries and batteries having a low active mass loss, the discharge of the battery is essentially limited by the acid contained in the electrolyte (acid limitation). For the acid concentration at the location of the reaction (electrodes), the electrolyte voltage U_(e) proportional to this acid concentration is used in the charge predictor's calculation of the charge able to be drawn. Typical boundary values for new batteries are e.g. U_(e,krit), acid=11.5 V at discharge termination (see branch b in FIG. 4).

5.2. Active Mass Limitation

In the case of batteries having a higher active mass loss, the discharge termination (the battery no longer provides any charge) sets in already at higher voltages due to the depletion of the active mass (Pb, PbO₂) available for the discharge reaction. FIG. 4 shows this shift of the critical electrolyte voltage U_(e,krit) by a value ΔU_(e,grenz) in the direction of higher voltages (from 11.5 to 12V; from branch b to branch c). Hence, taking into account the active mass limitation, the following relationship can be applied: U _(e,krit,Masse)=11.5 V+Δ_(Ue,grenz) 5.3. Electrolyte Icing

At temperatures below −10° C., electrolyte icing may occur particularly in the case of a low acid concentration. In this case, the supply of acid to the location of the reaction at the electrodes is inhibited such that a low acid concentration exists at the electrodes (see branch a in FIG. 4). For the critical electrolyte voltage, the following temperature-dependent relationship may be assumed: U _(e,krit,Eis)(T _(Batt))=11.423V−0.0558V*(T _(Batt)/° C.)−0.0011V*(T _(Batt)/° C.)²−1.0*e−5V*(T _(Batt)/° C.)³

Taking all three effects into account, the following relationship can be used for the first cutoff criterion (reaching a minimum electrolyte voltage U_(e)) U _(e) =U _(e,krit)=max(U _(e,krit,S{overscore (a)}ure) ,U _(e,krit,Masse) ,U _(e,krit,Eis))

FIG. 4 again shows the resulting characteristic of critical electrolyte voltage U_(e,krit) as a function of battery temperature T_(Batt) and ΔU_(e,grenz). 

1-10. (canceled)
 11. A device for ascertaining an amount of charge that is able to be drawn from an energy storage unit, up to at least one specified cutoff threshold, comprising: a charge predictor for calculating, in the case of a specified discharge current characteristic, the amount of charge that is able to be drawn from the energy storage unit, on the basis of a mathematical energy storage model that mathematically represents electrical properties of the energy storage unit; and an estimator for ascertaining at least one of state variables and parameters for the mathematical energy storage model, based on operating performance quantities of the energy storage unit.
 12. The device as recited in claim 11, wherein the energy storage unit is a battery, and wherein the mathematical energy storage model is a battery model that includes at least a mathematical model for an internal resistance, an acid diffusion resistance, and a charge transfer polarization.
 13. The device as recited in claim 12, wherein the estimator ascertains at least an open-circuit voltage and a concentration polarization as the state variables.
 14. The device as recited in claim 13, wherein the estimator additionally ascertains a charge transfer polarization.
 15. The device as recited in claim 12, wherein the charge predictor ascertains an amount of charge that is able to be drawn until a specified minimum electrolyte voltage that represents a first cutoff criterion is reached.
 16. The device as recited in claim 15, wherein the charge predictor ascertains an amount of charge that is able to be drawn until a specified minimum voltage of the energy storage unit that represents a second cutoff criterion is reached.
 17. The device as recited in claim 16, wherein the charge predictor ascertains an amount of charge that is able to be drawn until a specified minimum capacity that represents a third cutoff criterion is reached.
 18. The device as recited in claim 12, further comprising: a voltage predictor for ascertaining, as a function of a load current characteristic that is specified, a corresponding load voltage that arises on the basis of the specified load current characteristic.
 19. A method for ascertaining an amount of charge that is able to be drawn from an energy storage unit, up to at least one specified cutoff threshold, comprising: calculating, using a charge predictor, in the case of a specified discharge current characteristic, the amount of charge that is able to be drawn from the energy storage unit, on the basis of a mathematical energy storage model that mathematically represents electrical properties of the energy storage unit, wherein the energy storage unit is a battery; and ascertaining, using an estimator, at least one of state variables and parameters for the mathematical energy storage model, based on operating performance quantities of the energy storage unit.
 20. The method as recited in claim 19, wherein the charge predictor calculates an amount of charge that is able to be drawn until a specified minimum capacity that represents a cutoff criterion is reached, and wherein the charge predictor takes into account a load voltage supplied to the charge predictor by a voltage predictor, the voltage predictor ascertaining the load voltage as a function of a specified load current characteristic. 